I had some trouble to understand the code, and to understand what you demand. But this is somehow working:

1. PImage[] img;
2. PImage bg;
3. boolean doorContactOpening = false; // variables for the door sensors.
4. boolean doorContactClosing, runOnce = false;
5. int openDoor = 0; // variable for the degree of which the door is open
6. int doorSpeed = 3; // Setting the speed of the doors
7. long lastUpdate;
8. int currentImage = 1;
9. int a;
10. void setup() {
11.   size(730, 547);
12.   frameRate(30);
13.   bg = loadImage("http://i.imgur.com/vtnt2.jpg");
14.   img = new PImage[10]; 
15.   img[0] = loadImage("http://i.imgur.com/QiTjs.gif");  // Load the images into the program
16.   img[1] = loadImage("http://i.imgur.com/bdpXU.jpg");
17.   img[2] = loadImage("http://i.imgur.com/4U90P.jpg");
18.   img[3] = loadImage("http://i.imgur.com/GUtN8.jpg");
19.   img[4] = loadImage("http://i.imgur.com/PIiOd.jpg");
20.   img[5] = loadImage("http://i.imgur.com/SEyLo.jpg");
21.   img[6] = loadImage("http://i.imgur.com/wdyWo.jpg");
22.   img[7] = loadImage("http://i.imgur.com/idRl7.jpg");
23.   img[8] = loadImage("http://i.imgur.com/yDued.jpg");
24.   img[9] = loadImage("http://i.imgur.com/xxP4Z.jpg");
25.   lastUpdate = millis();
26. }
27. void draw() {
28.   background(0);
29.   image(bg, 0, 0);
30.   if (openDoor >= (width/2) && runOnce == true) {
31.     //currentImage = int(random(0, 5));
32.     bg = img[(int) random(10)];
33.     runOnce = false;
34.   }
35.   a = (a + 1)%(width+32);
36.   stroke(640, 460, 0);
37.   line(0, a, width, a-26);
38.   line(0, a-6, width, a-32);
39.   if (millis()-lastUpdate > 1) {
40.     if (doorContactOpening == true) {
41.       if (openDoor<(width/2)) {
42.         openDoor += doorSpeed;
43.       }   
44.       image(img[currentImage*2], -openDoor, 0);
45.       image(img[currentImage*2+1], (width/2)+openDoor, 0);
46.     }
47.     else if (doorContactClosing == true) {
48.       if (openDoor>0) {
49.         openDoor -= doorSpeed;
50.       }   
51.       image(img[currentImage*2], -openDoor, 0);
52.       image(img[currentImage*2+1], (width/2)+openDoor, 0);
53.     }
54.     else {
55.       image(img[currentImage*2], -openDoor, 0);
56.       image(img[currentImage*2+1], (width/2)+openDoor, 0);
57.     }
58.     lastUpdate = millis();
59.   }
60.   else {
61.     image(img[currentImage*2], -openDoor, 0);
62.     image(img[currentImage*2+1], (width/2)+openDoor, 0);
63.   }
64. }
65. void keyPressed() {
66.   if ( key == 'o') {
67.     doorContactClosing = false;
68.     doorContactOpening = true;
69.     runOnce = true;
70.   }
71.   else if ( key == 'c') {
72.     doorContactOpening = false;
73.     doorContactClosing = true;
74.   }
75. }

It's smarter to use different states instead of using 'IF' statements into (void) draw. A good example can be found here:
https://forum.processing.org/topic/best-practice-for-application-with-multiple-states


 

First of all, i really appriciate your help and you almost solved my problem! The problem is, that the two sliding images will be following an electronic door, and when the door opens, an image that is related to the two sliding images is projected onto a wall behind the doors. 

Actually, after studying and changing some settings in your code, I have realized that it is fully useful. The only mistake is that the two sliding images also functions as background images. If it is possible to exclude these two images from the stack of background images it would be perfect. Hope you can help!